Stability and Performance Verification of Dynamical Systems Controlled by Neural Networks: Algorithms and Complexity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00360191" target="_blank" >RIV/68407700:21230/22:00360191 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1109/LCSYS.2022.3181806" target="_blank" >https://doi.org/10.1109/LCSYS.2022.3181806</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/LCSYS.2022.3181806" target="_blank" >10.1109/LCSYS.2022.3181806</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Stability and Performance Verification of Dynamical Systems Controlled by Neural Networks: Algorithms and Complexity

Popis výsledku v původním jazyce

This letter makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a neural network with semialgebraically representable activation functions (e.g., ReLU) can be certified by convex semidefinite programming. The result is based on the fact that the semialgebraic representation of the activation functions and polynomial dynamics allows one to search for a Lyapunov function using polynomial sum-of-squares methods. Second, we remark that even in the case of a linear system controlled by a neural network with ReLU activation functions, the problem of verifying asymptotic stability is undecidable. Finally, under additional assumptions, we establish a converse result on the existence of a polynomial Lyapunov function for this class of systems. Numerical results with code available online on examples of state-space dimension up to 50 and neural networks with several hundred neurons and up to 30 layers demonstrate the method.

Název v anglickém jazyce

Stability and Performance Verification of Dynamical Systems Controlled by Neural Networks: Algorithms and Complexity

Popis výsledku anglicky

This letter makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a neural network with semialgebraically representable activation functions (e.g., ReLU) can be certified by convex semidefinite programming. The result is based on the fact that the semialgebraic representation of the activation functions and polynomial dynamics allows one to search for a Lyapunov function using polynomial sum-of-squares methods. Second, we remark that even in the case of a linear system controlled by a neural network with ReLU activation functions, the problem of verifying asymptotic stability is undecidable. Finally, under additional assumptions, we establish a converse result on the existence of a polynomial Lyapunov function for this class of systems. Numerical results with code available online on examples of state-space dimension up to 50 and neural networks with several hundred neurons and up to 30 layers demonstrate the method.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koncept Koopmanova operátoru pro řízení komplexních nelineárních dynamických systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Control Systems Letters

ISSN

2475-1456

e-ISSN

2475-1456

Svazek periodika

6

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

6

Strana od-do

3265-3270

Kód UT WoS článku

000819822000002

EID výsledku v databázi Scopus

2-s2.0-85132740353